DLMF:14.12.E5 (Q4826): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
Defining formula:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1ddec

Latest revision as of 01:43, 2 January 2020

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DLMF:14.12.E5
No description defined

    Statements

    Defining formula
    P ν - μ ⁡ ( x ) = ( x 2 - 1 ) - μ / 2 Γ ⁡ ( μ ) ⁢ ∫ 1 x P ν ⁡ ( t ) ⁢ ( x - t ) μ - 1 ⁢ d t , Legendre-P-first-kind 𝜇 𝜈 𝑥 superscript superscript 𝑥 2 1 𝜇 2 Euler-Gamma 𝜇 superscript subscript 1 𝑥 Legendre-spherical-polynomial 𝜈 𝑡 superscript 𝑥 𝑡 𝜇 1 𝑡 {\displaystyle{\displaystyle P^{-\mu}_{\nu}\left(x\right)=\frac{\left(x^{2}-1% \right)^{-\mu/2}}{\Gamma\left(\mu\right)}\int_{1}^{x}P_{\nu}\left(t\right)(x-t% )^{\mu-1}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:14.12.E5
    0 references
    constraint
    ℜ ⁡ μ > 0 𝜇 0 {\displaystyle{\displaystyle\Re\mu>0}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
    0 references
    Q11481
    Defining formula
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1aadec
    0 references
    Q10920
    Defining formula
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1addec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1bdec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1ddec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1ddec
    0 references
     
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